Probing the Origin of the Open Circuit Voltage in Perovskite Quantum Dot Photovoltaics

Perovskite quantum dots (PQDs) have many properties that make them attractive for optoelectronic applications, including expanded compositional tunability and crystallographic stabilization. While they have not achieved the same photovoltaic (PV) efficiencies of top-performing perovskite thin films, they do reproducibly show high open circuit voltage (VOC) in comparison. Further understanding of the VOC attainable in PQDs as a function of surface passivation, contact layers, and PQD composition will further progress the field and may lend useful lessons for non-QD perovskite solar cells. Here, we use photoluminescence-based spectroscopic techniques to understand and identify the governing physics of the VOC in CsPbI3 PQDs. In particular, we probe the effect of the ligand exchange and contact interfaces on the VOC and free charge carrier concentration. The free charge carrier concentration is orders of magnitude higher than in typical perovskite thin films and could be tunable through ligand chemistry. Tuning the PQD A-site cation composition via replacement of Cs+ with FA+ maintains the background carrier concentration but reduces the trap density by up to a factor of 40, reducing the VOC deficit. These results dictate how to improve PQD optoelectronic properties and PV device performance and explain the reduced interfacial recombination observed by coupling PQDs with thin-film perovskites for a hybrid absorber layer.


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Where n/n t are electron densities in conduction band/trap state, N t is trap density, k 1 /k 2 /k 3 /k 4 are rate constants shown in Figure 3b. Following Ref.
2, for simplicity we did not consider hole trapping. Detrapping rate constant k 3 exponentially depends on the activation energy E a of the electron trap Where  n is cross-section, v th is thermal velocity, N C is density of states in the conduction band, k B is Boltzmann's constant, and T is temperature. PL intensity is calculated as a product of free electrons and free holes (ref. 2).
A more detailed TRPL model including radiative recombination is described below. Model of Eqs.
(S1) -(S3) has a smaller number of adjustable parameters and is easier to apply to the low injection data. Modeling is not very sensitive to rates k 2 and k 4 and assumed values for these parameters are k 2 −1 = 1 ns, and k 4 −1 = 100 ns. Simulated kinetic decays for CsPbI 3 PQDs are shown in Figure S1, and parameters used in kinetic simulations for CsPbI 3 , Cs 0.5 FA 0.5 PbI 3 , and FAPbI 3 are summarized in Table S3.
Experimental data is given in Figure 3a. Black solid line shows the lowest injection where photogenerated carrier density is lower than trap density. Purple and grey lines correspond to injection where photogenerated carrier density exceeds trap density. S10 Table S3. Defect-mediated recombination lifetimes, trap densities, and trap activation energies.
Kinetic parameters in used to simulate injection dependence for time integrated TRPL data, shown as solid lines in Fig. 3(b), Fig. 4(c), and Fig. 4(d). Representative TRPL data for CsPbI 3 PDQ films before ligand exchange ( Figure Sxa).
These samples have lower background carrier density (doping) and as a result, the TRPL data is dominated by radiative recombination in the experimentally accessible injection range. This is evident by the fact that the highest lifetime was obtained with the lowest excitation fluence, and lifetimes decrease when injection is increased. Please note the very different excitation fluence dependence for solid-state ligand exchanged samples (compared to Figure 3a in the manuscript).

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Time-integrated TRPL data ( Figure Sxb, also shown below) does not indicate the characteristic transition from empty to filled trap states (black versus green). Therefore, prior to solid state ligand exchange, we are not able to quantify either defect-mediated recombination lifetime, trap density, or background carrier density (doping).
Such samples have very different recombination properties, which is best illustrated by by their ~300 times higher radiative efficiency (Table S1). This TRPL data is in agreement with this result.

Kinetic model for high-injection TRPL data
As described in earlier section, modeling minority carrier dynamics (from low injection TRPL data) established bulk carrier lifetime, trap density and activation energy (Table S3). To analyze radiative recombination from high injection TRPL data both electron and hole dynamics need to be considered. We used a previously published MATLAB script 3 to solve time-dependent transport equations for electrons n (Eq. (S4)) and holes p (Eq. (S5)):

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(2)) was approximated by a Gaussian laser pulse with 300 fs width and Beer's law when absorber thickness was d = 300 nm and absorption coefficient 110 5 cm -1 . Figure S6. Kinetic scheme used in simulations of high injection TRPL data.